Question

What is the current through the 1-Ohm resistor in this circuit?

Help. Explain AND answer w diagram please

Answer 1

Now focus on the loop on extreme left or loop 1.

To apply KVL, choose to transverse the loop in the clockwise sense and adopt the following sign conventions

1 The emfs of cells are taken to be negative if the negative poles are encountered first and vice versa.

2 The products of currents and resistances are taken to be positive if flow of currents is in the same sense in which we are to transverse the loop and vice versa.

And hence

6 - 4 I₁ – (I₁ + I₂) = 0

5 I₁ + I₂ = 6 ……………………………………… (1)

Similarly for next loop or loop 2

-9 + (I₁ + I₂) + 2 I₂ = 0

I₁ + 3I₂ = 9 ……………………………………… (2)

So now we have a system of linear equations as

5 I₁ + I₂ = 6 ……………………………………… (1)

I₁ + 3I₂ = 9 ……………………………………… (2)

On solving the above system of equations, we get

I₁ = 0.6429 A

I₂ = 2.7857 A

So current through 1 ohm resister = 0.6429 A + 2.7857 A = 3.4286 A